The country currently holds the European Union’s revolving six-month Presidency, which leaves it with the often thankless tasks of forging compromises on proposed laws among the bloc’s member states. One of the big ones on Lithuania’s to-do list before the end of the year is a proposal for a single resolution mechanism, which will centralize control of failing banks — the next step in the euro zone’s banking union project.

The fear is that under the current plan, a government could be forced to spend money winding down one of its banks against its will.

This week, Lithuania made its first attempt at finding a compromise on the proposal. At a meeting in Brussels on Wednesday, the country’s ambassador handed his counterparts a list of five possible options to better protect national budgets.

The first option was to grant member states a veto over decisions that would require them to spend money on the resolution or restructuring of one of their banks. That proposal — broadly supported by Luxembourg, the Netherlands, Slovakia and Estonia, according to an EU official — would settle the legal issue. But it would undermine one of the central goals of creating a single resolution mechanism, namely to eliminate national bias in resolution decisions.

A less radical variant — broadly backed by France, Ireland, Cyprus, Latvia and Poland — would give the affected state’s vote more weight in decisions on the resolution board. However, some ambassadors worry that doesn’t go far enough to protect states’ control over their budgets.

A third option was to bring forward the date from which even senior bond holders and large depositors would have to take losses when a bank runs into trouble – a move that could sharply cut the cost of resolution.

Under separate legislation, that is also still being negotiated, this so-called “bail-in” wouldn’t start until 2018. Lithuania suggested bringing the start-date forward to 2015, when the single resolution mechanism is due to kick in. That option was broadly supported by the European Central Bank, Denmark, the Netherlands and Germany, according to an EU official. In fact, Berlin wants the tougher stance on bail-in to come in combination with a veto right, or weighted voting, the official said.

Two other options proposed by Lithuania were less popular. One was to rein in the powers of the central resolution board, where member states would be represented by their national resolution authorities, by requiring finance ministers to decide on any use of common funds. The other was to create an independent mediation panel that would rule in any case where a member state disagreed with the resolution board’s decision. Nobody liked that plan.

Many ambassadors favored a combination of options, or thought that all needed more work. Lithuania will return with revamped proposals on Oct. 17 and Oct. 18. One thing is clear: The country’s officials will need all their strength to see this through.

About Real Time Brussels

The Wall Street Journal’s Brussels blog is produced by the Brussels bureau of The Wall Street Journal and Dow Jones Newswires. The bureau has been headed since 2009 by Stephen Fidler, who was previously a correspondent and editor for the Financial Times and Reuters. Also posting regularly: Matthew Dalton, Viktoria Dendrinou, Tom Fairless, Naftali Bendavid, Laurence Norman, Gabriele Steinhauser and Valentina Pop.